Should I use Blender 2.44 rather than the latest version of Blender?
Downsides to using blender version 2.49 or older:


Interface is very different than versions after 2.5
Materials are set up differently, some of the functions have other names.
Animation and rigging will not translate properly to newer versions.
Keyboard shortcuts are different.
Most modern plugins will not work. Python scrip terms and versions might not be compatible.
Unstable, and has more bugs.
Possible incompatibilities using modern hardware or modern Operating Systems
No Cycles rendering possible.
Lacks major features to reduce time consuming tasks.
Some tutorials will use features you have, but you will have trouble finding them.
Many users on BSE, and on-line forums will not be unable to help you, as a lot of use never used that version (Surely a few have though)
Harder to find support. 
If you find a bug, or blender crashes, you cannot report the crash/bug, and will have to find really old topics for help, or just end up working around the bug.
Generally not a good idea
Once you master the old version, you'll have to forget what you've learned and start over to learn newer versions.


Upsides to using older version:


Perhaps some features you loved are there that they removed (and if there is you can probably find someone made it into a plugin somewhere)


some plugins for older formats only work on older versions.

A different look. 


Feel free to edit in other upsides/downsides.